# Algebraic Expressions

Exercise 1

1. Identify the terms, their coefficients for each of the following expressions.

(i) 5xyz2 – 3zy

Answer: Term: xyz2 -- Coefficient = 5

Term: zy –- Coefficient = 3

(ii) 1 + x + x2

Answer: Term: x – Coefficient = 1 & Term: x2 – Coefficient = 1

(iii) 4x2y2 – 4x2y2z2 + z2

Answer: 4 is the coefficient for x2y2z2

1 is the term for z2

(iv) 3 – pq + qr – rp

Answer: For each term the coefficient is 1

(v) Answer: ½ is the coefficient for x and y and for xy it is 1

(vi) 0.3a – 0.6ab + 0.5b

Answer: 0.3 is the coefficient for a, for b there are two coefficients 0.6 and 0.5

2. Classify the following polynomials as monomials, binomials, trinomials. Which polynomials do not fit in any of these three categories?

x + y: Binomial

1000: Mononomial

x + x2 + x3 + x4: Polynomial

7 + y + 5x: Binomial

2y – 3y2: Binomial

2y – 3y2 + 4y3: Trinomial

5x – 4y + 3xy: Trinomial

4z – 15z2: Binomial

ab + bc + cd + da: Polynomial

pqr: Mononomial

p2q + pq2: Binomial

2p + 2q: Binomial

(i) ab – bc, bc – ca, ca – ab

Answer: (ab - bc) + (bc - ca) + (ca-ab)

=ab + bc + ca - bc - ca - ab

= 0

(ii) a – b + ab, b – c + bc, c – a + ac

Answer: (a - b + ab) + (b - c + bc) + (c - a + ac)

= a + b + c + ab + bc + ca - b - c - a

= ab + bc + ca

(iii) 2p2q2 – 3pq + 4, 5 + 7pq – 3p2q2

= (2p2q2 - 3pq + 4) + (5 + 7pq - 3p2q2)

= 2p2q2 - 3p2q2 - 3pq + 7pq + 4 + 5

= - p2q2 + 4pq + 9

(iv) l2 + m2, m2 + n2, n2 + l2, 2lm + 2mn + 2nl

Answer: (l2 + m2) + (m2 + n2) + (n2 + l2) + (2lm + 2mn + 2nl)

= l2 + l2 + m2 + m2 + n2 + n2 + 2lm + 2mn + 2nl

= 2l2 + 2m2 + 2n2 + 2lm + 2mn + 2nl

4. (a) Subtract 4a – 7ab + 3b + 12 from 12a – 9ab + 5b – 3

Answer: (12a - 9ab + 5b - 3) - (4a - 7ab + 3b + 12)

= 12a - 9ab + 5b - 3 - 4a + 7ab - 3b - 12

(signs are reversed after –sign once bracket is opened)

= 8a - 2ab + 2b - 15

(b) Subtract 3xy + 5yz – 7zx from 5xy – 2yz – 2zx + 10xyz

Answer: (5xy - 2yz - 2zx + 10xyz) - (3xy + 5yz - 7zx)

= 5xy - 2yz - 2zx + 10xyz - 3xy - 5yz + 7zx

= 2xy - 7yz + 5zx + 10xyz

(c) Subtract 4p2q – 3pq + 5pq2 – 8p + 7q – 10

from 18 – 3p – 11q + 5pq – 2pq2 + 5p2q

Answer: (18 - 3p - 11q + 5pq - 2pq2 + 5p2q) - (4p2q - 3pq + 5pq2 - 8p + 7q - 10)

= 18 - 3p - 11q + 5pq - 2pq2 + 5p2q - 4p2q + 3pq - 5pq2 + 8p - 7q + 10

= 28 + 5p - 18q + 8pq - 7pq2 - p2q

Algebraic Expressions will be available online in PDF book form soon. The solutions are absolutely Free. Soon you will be able to download the solutions.